The score resets when scene resets
you can use a Game actuator, load global dict and save global dict, i dont know how this actuator works. i think you'll need little bit of python to do this.
google for "bge global-dict". there are a few tutorials on youtube.
or you can just create a file. 
with open("file", "w") as f: f.write() f.close(), 
save the file a openit up from other scene. 
with open("file", "r") as f: f.readLine() f.read()... and so.
It's basically the same thing. A dict that blender handles or a "dict" you handle.